City Council Speaker Christine Quinn officially launched her bid to become the city’s first female and openly gay mayor yesterday — and one of her rivals, Public Advocate Bill de Blasio, countered by trotting out his own celebrity lesbian backer.

“That’s the ultimate truth about New York, that it needs to remain and become even more that place of opportunity, a place that’s a beacon for the middle class and people who are fighting so hard to get into the middle class,” she told supporters in Inwood.

Joined by her wife, Kim Catullo, Quinn announced her candidacy across the street from Capuchin Franciscans of the Good Shepherd Church, where her parents were married.

She followed with stops in every borough.

Democratic rival de Blasio was in lower Manhattan to kick off his Women for de Blasio campaign with 200 supporters, led by “Sex and the City” star Cynthia Nixon, a lesbian and gay-rights activist.

“We need a mayor that sees New York City as more than the Upper East Side of Manhattan,” Nixon said in a jab at Mayor Bloomberg, a Quinn ally.

And she blasted Quinn for backing the mayor’s successful bid in 2008 to overturn term limits through the council.

“We need a mayor that doesn’t blatantly disregard term limits!” she said.

De Blasio attacked Quinn’s refusal to bring to a vote a bill that would force private businesses to offer paid days off.

“I don’t know many people in New York who can afford missing a day or two of work just for being sick,” he said.

Quinn said yesterday that the bill would be too hard on small businesses.

On Southern Boulevard in The Bronx yesterday, she hopped on a city bus to say hi to riders.

“She’s got my vote and everybody who gets on my bus!” said the driver, William Adams.

But she was heckled in Forest Hills, Queens, for extending term limits.